On the analysis of a dynamical model representing gene regulatory networks under negative feedback

Abstract

SUMMARYIn this work, stability analysis is performed for a cyclic dynamical model of gene regulatory networks involving time delays, under negative feedback. The model considered has nonlinearities with negative Schwarzian derivatives. Sufficient conditions implying global stability of these types of GRNs are obtained. The special case of homogenous gene regulatory networks is also studied; in this case, the proposed stability conditions depend only on the parameters of the nonlinearity function. Illustrative numerical examples complete the presentation.

Analysis of Deterministic Cyclic Gene Regulatory Network Models with Delays

“…Moreover, lower and upper bounds on the magnitude of the periodic oscillations are given when the system is not stable. Most of the results presented in Chapter 5 are based on our recent work [1]. In Chapter 6, the ODE-based GRN model is studied under positive feedback.…”

“…Proper analysis of gene expression data may give us useful insights about the changes in the regulatory networks that may lead to 1 7 diseases. For example, parts of the regulatory network between a normal person and a cancer patient might be quite different.…”